Finite Group Databasebeta

← #14642116

Subgroups — #14642116

Order 2816.

432 conjugacy classes of subgroups; only the 107 normal subgroups are shown.

normal subgroups only

This group has 432 conjugacy classes of subgroups — too many to draw. Only its 107 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13076988C211yesmaximal, characteristic
2#13068362C211yesmaximal, characteristic, complemented
3#13066441C212yesmaximal, complemented
4#13066436C212yesmaximal
5C11×#1839C211yesmaximal, characteristic, complemented
6C2×#66928C411yescharacteristic
7C2×#66923C411yescharacteristic
8C43×C11C2211yescharacteristic
9#10622553—21no—
10#10622553—21no—
11#10622553—21no—
12#10622553—21no—
13#10622552C411yescharacteristic
14#10622552C2211yescharacteristic
15#10622542C411yescharacteristic
16#10622542C2211yescharacteristic
17C2×C4×C11⋊C8—21no—
18C11×#336—21no—
19C11×#336—21no—
20C11×#336C2212yes—
21#10622162—21no—
22#10622162C2212yes—
23C22×D44C2×C411yescharacteristic
24C22×Dic22C2×C411yescharacteristic
25C22×C8×C11—22no—
26C2×C42×C11C2×C411yescharacteristic
27C2×C42×C11C2×C411yescharacteristic
28C2×C42×C11D411yescharacteristic
29C2×C42×C11D411yescharacteristic
30C2×C42×C11D411yescharacteristic
31C2×C42×C11D411yescharacteristic
32C2×C42×C11C2311yescharacteristic
33C2×(C2×D11)⋊C4—21no—
34C2×(C2×D11)⋊C4—21no—
35C2×(C2×D11)⋊C4—21no—
36C2×(C2×D11)⋊C4—21no—
37C2×(C2×D11)⋊C4—21no—
38C2×(C2×D11)⋊C4—21no—
39C2×C4⋊Dic11C2×C411yescharacteristic
40C2×C4⋊Dic11C2×C411yescharacteristic
41C2×Dic11⋊C4—21no—
42C2×Dic11⋊C4—21no—
43C22×C11⋊C8—22no—
44#66928—42no—
45#66923—42no—
46C11⋊#95—21no—
47C11⋊#95—21no—
48C11⋊#95—21no—
49C11⋊#95—21no—
50C4×C11⋊C8—24no—
51#7656—111nomaximal, Sylow
52C23×D11—21no—
53C22×C4×C11C22⋊C411yescharacteristic
54C22×C4×C11C22⋊C411yescharacteristic
55C22×C4×C11C22⋊C411yescharacteristic
56C22×C4×C11C22⋊C411yescharacteristic
57C22×C4×C11C22×C411yescharacteristic
58C22×C4×C11C2×D411yescharacteristic
59C22×C4×C11C2×D411yescharacteristic
60C22×Dic11—21no—
61C22×Dic11—21no—
62C22×Dic11—21no—
63C2×D44—22no—
64C2×D44—41no—
65C2×D44—41no—
66C2×Dic22—22no—
67C2×Dic22—41no—
68C2×Dic22—41no—
69C2×C8×C11—42no—
70C2×C8×C11—42no—
71C2×C8×C11—42no—
72C42×C11—22no—
73C42×C11—22no—
74C42×C11—22no—
75C42×C11—22no—
76C42×C11—22no—
77C42×C11—41no—
78C42×C11—41no—
79(C2×D11)⋊C4—42no—
80(C2×D11)⋊C4—42no—
81(C2×D11)⋊C4—42no—
82(C2×D11)⋊C4—42no—
83(C2×D11)⋊C4—42no—
84(C2×D11)⋊C4—42no—
85C4⋊Dic11—41no—
86C4⋊Dic11—41no—
87Dic11⋊C4—42no—
88Dic11⋊C4—42no—
89C2×C11⋊C8—24no—
90C2×C11⋊C8—42no—
91C2×C11⋊C8—42no—
92#2861—111no—
93#1839D1111yescharacteristic, complemented
94#1744—111no—
95#1272—112no—
96#1270—112no—
97C23×C11C2×C22⋊C411yescharacteristic
98C22×D11—41no—
99C22×D11—41no—
100C22×D11—41no—
101C22×D11—41no—
102C22×D11—41no—
103C22×D11—41no—
104C22×D11—41no—
105C2×C4×C11—21no—
106C2×C4×C11—21no—
107C2×C4×C11—21no—
108C2×C4×C11—21no—
109C2×C4×C11—21no—
110C2×C4×C11—21no—
111C2×C4×C11—21no—
112C2×C4×C11—21no—
113C2×C4×C11—21no—
114C2×C4×C11—21no—
115C2×C4×C11—21no—
116C2×C4×C11—21no—
117C2×C4×C11—21no—
118C2×C4×C11—21no—
119C2×C4×C11—21no—
120C2×C4×C11—21no—
121C2×C4×C11#10012yes—
122C2×C4×C11#10412yes—
123C2×C4×C11#13112yes—
124C2×C4×C11#13512yes—
125C2×C4×C11#13512yes—
126C2×Dic11—41no—
127C2×Dic11—41no—
128C2×Dic11—41no—
129C2×Dic11—41no—
130C2×Dic11—41no—
131C2×Dic11—41no—
132C2×Dic11—41no—
133C2×Dic11—41no—
134C2×Dic11—41no—
135D44—82no—
136Dic22—82no—
137C8×C11—82no—
138C11⋊C8—44no—
139C2×#125—111no—
140C2×#124—111no—
141C2×C4×C8—221no—
142#391—111no—
143#391—111no—
144#390—111no—
145#390—111no—
146#388—221no—
147#388—221no—
148#388—221no—
149#388—221no—
150C43C2×D1111yescharacteristic
151#336—21no—
152#336—21no—
153#336—112no—
154#336—221no—
155#336C2×D1112yes—
156C22×C11#40811yescharacteristic
157C22×C11#41011yescharacteristic
158C22×C11C2×#10011yescharacteristic
159C22×C11#41611yescharacteristic
160C22×C11#41611yescharacteristic
161C22×C11C2×#10411yescharacteristic
162C22×C11#42111yescharacteristic
163C2×D11—81no—
164C2×D11—81no—
165C2×D11—81no—
166C2×D11—81no—
167C2×D11—81no—
168C2×D11—81no—
169C2×D11—81no—
170C4×C11—22no—
171C4×C11—22no—
172C4×C11—22no—
173C4×C11—22no—
174C4×C11—22no—
175C4×C11—41no—
176C4×C11—41no—
177Dic11—81no—
178Dic11—81no—
179Dic11—81no—
180C22×Q8—111no—
181C22×D4—111no—
182C22×C8—22no—
183C22×C8—222no—
184#125—442no—
185#124—442no—
186C2×C4⋊C4—111no—
187C2×C4⋊C4—111no—
188C2×C4⋊C4—221no—
189C2×C4⋊C4—221no—
190C2×C22⋊C4—221no—
191C2×C22⋊C4—221no—
192C2×C22⋊C4—221no—
193C2×C22⋊C4—221no—
194C2×C22⋊C4—221no—
195C2×C22⋊C4—221no—
196C2×C42C4×D1111yescharacteristic
197C2×C42C4×D1111yescharacteristic
198C2×C42D4411yescharacteristic
199C2×C42D4411yescharacteristic
200C2×C42C22⋊D1111yescharacteristic
201C2×C42C22⋊D1111yescharacteristic
202C2×C42C22×D1111yescharacteristic
203C4×C8—224no—
204#95—221no—
205#95—221no—
206#95—221no—
207#95—221no—
208C2×C11#146911yescharacteristic
209C2×C11#148211yescharacteristic
210C2×C11#149411yescharacteristic
211C2×C11#150011yescharacteristic
212C2×C11#152111yescharacteristic
213C2×C11#153011yescharacteristic
214C2×C11#154311yescharacteristic
215D11—161no—
216C24—221no—
217C2×Q8—222no—
218C2×Q8—441no—
219C2×Q8—441no—
220C2×D4—222no—
221C2×D4—441no—
222C2×D4—441no—
223C22×C4—221no—
224C22×C4—221no—
225C22×C4—221no—
226C22×C4(C2×D11)⋊C411yescharacteristic
227C22×C4(C2×D11)⋊C411yescharacteristic
228C22×C4(C2×D11)⋊C411yescharacteristic
229C22×C4(C2×D11)⋊C411yescharacteristic
230C22×C4C2×C4×D1111yescharacteristic
231C22×C4C2×D4411yescharacteristic
232C22×C4C2×C22⋊D1111yescharacteristic
233C2×C8—42no—
234C2×C8—42no—
235C2×C8—42no—
236C2×C8—224no—
237C2×C8—442no—
238C2×C8—442no—
239C4⋊C4—441no—
240C4⋊C4—441no—
241C4⋊C4—442no—
242C4⋊C4—442no—
243C22⋊C4—442no—
244C22⋊C4—442no—
245C22⋊C4—442no—
246C22⋊C4—442no—
247C22⋊C4—442no—
248C22⋊C4—442no—
249C42—22no—
250C42—22no—
251C42—22no—
252C42—22no—
253C42—22no—
254C42—41no—
255C42—41no—
256C11#765611yescharacteristic, complemented, Sylow
257C23—441no—
258C23—441no—
259C23—441no—
260C23—441no—
261C23—441no—
262C23—441no—
263C23—441no—
264C23C2×(C2×D11)⋊C411yescharacteristic
265Q8—882no—
266D4—882no—
267C2×C4—21no—
268C2×C4—21no—
269C2×C4—21no—
270C2×C4—21no—
271C2×C4—21no—
272C2×C4—21no—
273C2×C4—21no—
274C2×C4—21no—
275C2×C4—21no—
276C2×C4—21no—
277C2×C4—21no—
278C2×C4—21no—
279C2×C4—21no—
280C2×C4—21no—
281C2×C4—21no—
282C2×C4—21no—
283C2×C4—441no—
284C2×C4—441no—
285C2×C4—441no—
286C2×C4—441no—
287C2×C4—441no—
288C2×C4—441no—
289C2×C4—441no—
290C2×C4—441no—
291C2×C4—441no—
292C2×C4#6688712yes—
293C2×C4#6688912yes—
294C2×C4#6695712yes—
295C2×C4#6696012yes—
296C2×C4#6700312yes—
297C8—82no—
298C8—444no—
299C22—881no—
300C22—881no—
301C22—881no—
302C22—881no—
303C22—881no—
304C22—881no—
305C22—881no—
306C22#1062261511yescharacteristic
307C22#1062261811yescharacteristic
308C22#1062261911yescharacteristic
309C22#1062272611yescharacteristic
310C22#1062274211yescharacteristic
311C22C2×#6688711yescharacteristic
312C22C2×#6688911yescharacteristic
313C4—22no—
314C4—22no—
315C4—22no—
316C4—22no—
317C4—22no—
318C4—41no—
319C4—41no—
320C4—881no—
321C4—881no—
322C4—881no—
323C2—1761no—
324C2#1306696911yescharacteristic
325C2#1306702511yescharacteristic
326C2#1306707411yescharacteristic
327C2#1306710311yescharacteristic
328C2#1306719111yescharacteristic
329C2#1306722811yescharacteristic
330C2#1306727611yescharacteristic
subgroupG/H
centerC23C2×(C2×D11)⋊C4
commutatorC22×C4×C11C22×C4
FrattiniC2×C42C22×D11
FittingC11×#1839C2
socleC23×C11C2×C22⋊C4
prime radicalC22×D44C2×C4
cosocleC2×C42×C11C23
hypercenter#1839D11
hypocenterC11#7656
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C43 ◁ #1839

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
2. #13068362C2semidirect
3. #13066441C2semidirect
5. C11×#1839C2semidirect
93. #1839D11semidirect
256. C11#7656semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
#130769882
#130683622
#130664412
#130664362
C11×#18392
#765611